<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon">IT</font> =  <a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font>;<br/>
<b>let </b><font color="Maroon">p1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>, <font color="Maroon">p2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_3.html#D5" target="_self">ORDERS_3:def 5</a><br/>

<b>assume </b><a NAME="E1:23"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">p1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">p2</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">p1'</font> = <font color="Maroon">p1</font>, <font color="Maroon">p2'</font> = <font color="Maroon">p2</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E3:23"/><i><font color="Green">E21</font></i>: 
( <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1'</font> &amp; <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p2'</font> )
 
<b>by </b><i><a class="ref" href="tmap_1.html#T91">TMAP_1:91</a></i>;<br/>
<b>let </b><font color="Maroon">r1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>, <font color="Maroon">r2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E4:23"/>
( <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p1</font> &amp; <font color="Maroon">r2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">p2</font> )
 ;<br/>

<b>hence </b><a NAME="E5:23"/>
<font color="Maroon">r1</font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">r2</font>
 <b>by </b><i>, </i>;<br/>


</div>
